lean_workbook_plus_40462

Disproved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

It suffices to prove that $\frac {1}{{{a^3} + {b^2} + {c^2}}} + \frac {1}{{{b^3} + {c^2} + {a^2}}} + \frac {1}{{{c^3} + {a^2} + {b^2}}} \le \frac {3}{{{a^2} + {b^2} + {c^2}}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40462 : ∀ a b c : ℝ, (1 / (a ^ 3 + b ^ 2 + c ^ 2) + 1 / (b ^ 3 + c ^ 2 + a ^ 2) + 1 / (c ^ 3 + a ^ 2 + b ^ 2) ≤ 3 / (a ^ 2 + b ^ 2 + c ^ 2))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph